Classification is a fundamental task in pattern recognition. Linear discriminant analysis is often used for pattern recognition primarily because of its simplicity, consistent treatment, and performance.
Most of the existing work directed to the structural analysis of classes is based upon maximizing the ratio of the between-class scatter to the within-class scatter (this ratio is called the Fisher criterion). However, the singularity of the within-class scatter matrix (or its variants) usually leads to computational issues when performing the generalized eigen-value analysis that is performed to solve the linear discriminant problem. Recently, use of a discrepancy criterion (i.e., for maximizing the difference, rather than the ratio, between the between-class scatter and the within-class scatter) has been investigated to avoid the singularity problem of the Fisher criterion.